A judge will hold a hearing to determine whether to grant a new trial to Paul Daugerdas, a former lawyer at the defunct firm Jenkens & Gilchrist, and three others convicted in a 10-year tax-shelter scheme.

U.S. District Judge William Pauley in Manhattan said today he will hold an evidentiary hearing on the conduct of Catherine Conrad, Juror No. 1 in the 10-week trial. He didn’t set a date. The defendants claim Conrad hid details of her background from the court, including a law degree, at least four arrests and the fact that she was serving a sentence of probation for shoplifting.